Matrix GPBiCG algorithms for solving the general coupled matrix equations - Hajarian, Masoud (IET control theory & applications, 2015)
Linear matrix equations have important applications in control and system theory. In the study, we apply Kronecker product and vectorisation operator to extend the generalised product bi-conjugate gradient (GPBiCG) algorithms for solving the general coupled matrix equations ∑lj=1(A)i,1,jX1Bi,1,j+Ai,2,jX2Bi,2,j+…+Ai,l,jXi,l,j) = Di  for  i = 1,2,…,l (including the (coupled) Sylvester, the second-order Sylvester and coupled Markovian jump Lyapunov matrix equations). We propose four effective matrix algorithms for finding solutions of the matrix equations. Numerical examples and comparison with other well-known algorithms demonstrate the effectiveness of the proposed matrix algorithms.